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Wigner Distribution Function Approach to Dissipative Problems in Quantum Mechanics with emphasis on Decoherence and Measurement Theory

R. F. O'Connell
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Abstract

We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak coupling and long-time approximations are valid. However, we also show their limitations for the discussion of decoherence, which is generally a short-time phenomenon with decay rates typically much smaller than typical dissipative decay rates. We discuss two approaches to the problem both of which use a quantum Langevin equation (QLE) as a starting-point: (a) use of a reduced WDF but in the context of an exact master equation (b) use of a WDF for the complete system corresponding to entanglement at all times.

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R. F. O'Connell. 2003-11-12. Wigner Distribution Function Approach to Dissipative Problems in Quantum Mechanics with emphasis on Decoherence and Measurement Theory. https://doi.org/10.1088/1464-4266/5/3/369

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